Cryptology ePrint Archive: Report 2013/391

Abstract: The Even-Mansour (EM) encryption scheme received a lot of attention in the last couple of years due to its exceptional simplicity and tight security proofs.
The original $1$-round construction was naturally generalized into $r$-round structures with one key, two alternating keys, and completely independent keys.
In this paper we describe the first key recovery attack on the one-key 3-round version of EM which is asymptotically faster than exhaustive search
(in the sense that its running time is $o(2^n)$ rather than $O(2^n)$ for an $n$-bit key).
We then use the new cryptanalytic techniques in order to improve the best known
attacks on several concrete EM-like schemes. In the case of LED-128, the best previously known attack could only be applied to 6 of its 12 steps. In this paper we develop a new attack which increases the number of attacked steps to 8, is slightly faster than the previous attack on 6 steps, and uses about a thousand times less data.
Finally, we describe the first attack on the full $\mbox{AES}^{2}$ (which uses two complete AES-128 encryptions and three independent $128$-bit keys, and looks exceptionally strong) which is about 7 times faster than a standard meet-in-the-middle attack, thus violating its security claim.